Further analysis of scintillation index for a laser beam propagating through moderate-to-strong non-Kolmogorov turbulence based on generalized effective atmospheric spectral model

A new expression of the scintillation index(SI) for a Gaussian-beam wave propagating through moderate-to-strong non-Kolmogorov turbulence is derived, using a generalized effective atmospheric spectrum and the extended Rytov approximation theory. Finite inner and outer scale parameters and high wave number "bump" are considered in the spectrum with a generalized spectral power law in the range of 3–4, instead of the fixed classical Kolmogorov power law of 11/3. The obtained SI expression is then used to analyze the effects of the spectral power law and the inner scale and outer scale on SI under various non-Kolmogorov fluctuation conditions. These results will be useful in future investigations of optical wave propagation through atmospheric turbulence.     

Irradiance scintillation considering finite turbulence inner scale for optical wave propagating through weak non-Kolmogorov turbulence

The turbulence inner scale plays an important role in investigating the irradiance scintillation index for optical wave propagating through atmospheric turbulence. However, previous expressions of the irradiance scintillation index, which were derived based on the general non-Kolmogorov spectral model, did not consider the influences of finite turbulence inner scale. In this study, based on the generalized exponential spectral model for non-Kolmogorov atmospheric turbulence, theoretical expressions of the irradiance scintillation index are derived for plane and spherical optical waves propagating through weak turbulence. The new expressions have considered the influences of the finite turbulence inner scale and the receiver aperture on the irradiance scintillation index. Numerical simulations are performed to analyze these parameters’ influences.     

Temporal power spectral models of angle of arrival fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

Analytical expressions of the temporal power spectral models of angle of arrival （AOA） fluctuations are derived using the generalized exponential spectral model for optical waves propagating through weak non- Kolmogorov turbulence. Compared with expressions of temporal power spectral models derived from the general non-Kolmogorov spectral model, the new expressions consider the influences of the inner and outer scales of finite turbulence. Numerical calculations show that large outer scales of turbulence increase the value of the temporal power spectrum of AOA fluctuations in low-frequency regions.     

Analysis of the temporal power spectral models of angel of arrival fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

New analytical expressions for the temporal power spectral models of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak non-Kolmogorov turbulence. They consider the finite turbulence inner and outer scales, and have a general power law value in the range of 3–4 instead of the standard power law value of 11/3. The results derived in this work can reduce correctly to the previously published analytic expressions for the case of plane and spherical waves propagation through Kolmogorov turbulence case. These results are useful for the understanding the potential impact of derivations from the standard Kolmogorov spectrum.     

Experimental investigation on the scintillation index of vortex beams propagating in simulated atmospheric turbulence

The scintillation index of vortex beam in simulated atmospheric turbulence is experimentally investigated. The fluctuation of the intensity can be effectively reduced by vortex beams. In particular, the reduction of scintillation is more pronounced for vortex beams with larger topological charge.     

Average capacity of free-space optical systems for a partially coherent beam propagating through non-Kolmogorov turbulence

The performance of partially coherent free-space optical links is investigated in the moderate to strong fluctuation regime of non-Kolmogorov turbulence. The expressions for large- and small-scale log-irradiance flux variance are obtained in non-Kolmogorov turbulence. By employing the gamma-gamma distribution of irradiance fluctuations, the effects of spatial coherence of the source, index of non-Kolmogorov spectrum, and size of the receiver on channel capacity for horizontal links are discussed. Results show that channel capacity presents fluctuating behaviors with the variation of alpha for longer links and increases for alpha values higher than 11/3.     

Degree of polarization for quantum light field propagating through non-Kolmogorov turbulence

Nonclassical polarization properties of a quantum field propagating through non-Kolmogorov turbulence are studied in a turbulent atmosphere paraxial channel. The analytic equation for the quantum degree of polarization of linearly polarized light is obtained. It is shown by numerical simulation that the polarization fluctuations of the quantum field are a function of the turbulent strength, the photon number, the propagation distance, the fractal constant α and the coherence length ρ₀.     

Spreading of partially coherent polychromatic Hermite-Gaussian beams propagating through non-Kolmogorov turbulence

The spreading of partially coherent polychromatic Hermite-Gaussian (PCPHG) beams propagating through non-Kolmogorov turbulence is studied, where the effect of non-Kolmogorov turbulence and beam bandwidth on the beam width spreading and angular spread is stressed. It is shown that the variation of the relative beam width of PCPHG beams with the generalized exponent parameter of non-Kolmogorov turbulence is non-monotonic. The larger bandwidth of PCPHG beams is, the smaller the relative beam width and the smaller the relative angular spread. Therefore, PCPHG beams with larger bandwidth are less affected by non-Kolmogorov turbulence than those with smaller bandwidth. PCPHG beams are less sensitive to the effect of non-Kolmogorov turbulence than fully coherent polychromatic Hermite-Gaussian (FCPHG) beams and polychromatic Gaussian Schell-model (PGSM) beams. The results are illustrated by numerical examples and interpreted.     

Some limitations on optical communication reliability through Kolmogorov and non-Kolmogorov turbulence

In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received signal, affecting link performance.Influence of Kolmogorov and non-Kolmogorov turbulence statistics on laser communication links are analyzed for different propagation scenarios, and effects of different turbulence spectrum models on optical communication links are presented. Statistical estimates of the communication parameters such as the probability of fade (miss) exceeding a threshold dB level, the mean number of fades, and BER are derived and examples provided. The presented quantitative data suggest that the non-Kolmogorov turbulence effects on lasercom channels are more severe in many situations and need to be taken into account in wireless optical communication. Non-Kolmogorov turbulence is especially important for elevations above the boundary layer as well as for even low elevation paths over water.     

Measurements of atmospheric turbulence strength by coherent optical scintillation

Summary The strength of the atmospheric turbulence is measured by an optical scintillation method. The obtained quantity is the structure constant at optical frequencies. As all turbulence parameters, this quantity is strongly affected by meteorological and local conditions, therefore it is of interest to measure it in different conditions and locations. The present measurements were made to characterize the turbulence at Florence. Paper presented at the 1° Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, Rome, June 19–22, 1984.     

Extension of the van Cittert-Zernike theorem for completely polarized incoherent electromagnetic beam propagating through non-Kolmogorov turbulence

Based on the 2 × 2 cross-spectral density matrix, the van Cittert-Zernike extended theorem is developed for the completely polarized incoherent beams propagation through the paraxial non-Kolmogorov turbulence. On the consequence of the extended theorem and the definition of general spectral degree of cross-polarization of a beam, we found that the spectral degree of cross-polarization of the resultant field is independent of the refractive index structure constant of atmospheric turbulence. We investigated the influences of the propagation distance and the distance of two detection points on the degree of coherence and the spectral degree of cross-polarization.     

Performance of phase compensated coherent free space optical communications through non-Kolmogorov turbulence

The bit-error-rate (BER) performance of coherent free-space optical (FSO) links employing phase compensation techniques is investigated in weak non-Kolmogorov turbulence. Assuming that the amplitude fading and phase fluctuation follow lognormal model and Gaussian distribution respectively and using the expression of non-Kolmogorov turbulence in terms of Zernike polynomials, the signal-to-noise ratio (SNR) at the coherent receiver is analyzed and as a special case, a new closed-form expression using chi-square distribution is obtained. Thus, the influence of different compensation modes and normalized receiver diameter on BER performance is evaluated and an optimum normalized receiver diameter is suggested to achieve the minimum BER. Moreover, the impact of outer scale L₀ and the exponent value α in non-Kolmogorov spectrum is studied with the optimum diameter, which reveals that the BER has an obvious decrease with larger values of L₀ and α.     

A three-dimensional refractive index model for simulation of optical wave propagation in atmospheric turbulence

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed with using the so-called “split”-operator method, when the influence of the propagation medium’s refractive index inhomogeneities is accounted for only within a system of infinitely narrow layers (phase screens) where phase is distorted. Commonly, under certain assumptions, such phase screens are considered as mutually statistically uncorrelated. However, in several important applications including laser target tracking, remote sensing, and atmospheric imaging, accurate optical field propagation modeling assumes upper limitations on interscreen spacing. The latter situation can be observed, for instance, in the presence of large-scale turbulent inhomogeneities or in deep turbulence conditions, where interscreen distances become comparable with turbulence outer scale and, hence, corresponding phase screens cannot be statistically uncorrelated. In this paper, we discuss correlated phase screens. The statistical characteristics of screens are calculated based on a representation of turbulent fluctuations of three-dimensional (3D) refractive index random field as a set of sequentially correlated 3D layers displaced in the wave propagation direction. The statistical characteristics of refractive index fluctuations are described in terms of the von Karman power spectrum density. In the representation of these 3D layers by corresponding phase screens, the geometrical optics approximation is used.     

Effects of inner and outer scale on the modulation transfer function for a Gaussian wave propagating through anisotropic non-Kolmogorov turbulence

Both experimental results and empirical research have shown that the atmospheric turbulence can present the anisotropic property not only at a few meters above the ground but also at high altitudes of up to several kilometers. This paper investigates the modulation transfer function of a Gaussian beam propagating along a horizontal path in weak anisotropic non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized exponential spectrum for anisotropic turbulence, which includes the spectral power law value, the finite inner and outer scales of turbulence, the anisotropic factor, and other essential optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the anisotropic factor.     

Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the angular spread θ _sp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition of the intensity. However, the θ _sp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition of the cross-spectral density function. For the superposition of the cross-spectral density function, θ _sp of GSM array beams with smaller coherence length σ ₀, smaller waist width w ₀, smaller beam number N, and larger separation distance x _d are less affected by turbulence than of those with larger σ ₀,w ₀,N, and smaller x _d ; while, for the superposition of the intensity, the effect of turbulence on θ _sp is independent of N and x _d . In addition, the angular spread is nearly the same for the two types of superposition when σ ₀ or w ₀ is small enough, or x _d is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence.     

Effective Rayleigh range of Gaussian array beams propagating through atmospheric turbulence

The analytical expressions for the effective Rayleigh range z_R of Gaussian array beams in turbulence for both coherent and incoherent combinations are derived. It is shown that z_R of Gaussian array beams propagating through atmospheric turbulence depends on the strength of turbulence, the array beam parameters and the type of beam combination. For the coherent combination z_R decreases due to turbulence. However, for the incoherent combination there exists a maximum of z_R as the strength of turbulence varies. The z_R of coherently combined Gaussian array beams is larger than that of incoherently combined Gaussian array beams, but for the coherent combination case z_R is more sensitive to turbulence than that for the incoherent combination case. The larger the beam number is, the longer z_R is, and the more z_R is affected by turbulence. For the coherent combination z_R is not monotonic versus the relative beam separation distance, and the effect of turbulence on z_R is appreciable within a certain range of the relative beam separation distance.     

Directionality of partially coherent annular flat-topped beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of partially coherent annular flat-topped beams propagating through atmospheric turbulence is derived by using the integral transform technique. In comparison with previous work, the results obtained in this paper are more general. It is shown that, except for equivalent Gaussian Schell-model (GSM) beams as pointed out in Ref. [T. Shirai, A. Dogariu, E. Wolf, Opt. Lett. 28 (2003) 610], there also exist equivalent annular and non-annular beams which may generate the same directionality as the corresponding fully coherent Gaussian beam both in free space and in turbulence. The theoretical results are illustrated by numerical examples and interpreted physically.     

Polarization-induced reduction in scintillation of optical beams propagating in simulated turbulent atmospheric channels

It is experimentally demonstrated that the class of partially coherent, partially polarized optical beams can be efficiently used for reduction in scintillations on propagation through turbulent air. The experiment involving the electromagnetic beam generation and its interaction with turbulent air simulator is discussed in details. The collected data is in solid agreement with the recently published theoretical predictions.     

Intensity fluctuations of spherical acoustic waves propagating through thermal turbulence*

The intensity fluctuations of acoustic waves that propagate through thermal turbulence are investigated under well controlled laboratory conditions. Two heated grids in air are placed horizontally in a large anechoic room and the mixing of the free convection plumes above them generates a homogeneous isotropic random thermal field. The spectrum of refractive index fluctuations is accurately described by a modified von Karman model which takes into account the entire spectrum of turbulence. Experimental data are obtained by varying both the frequency of the spherical wave and the distance of propagation. In this paper we concentrate on the variance of the normalized intensity fluctuations and on their probability distributions. These measurements cover all the regimes from weak scattering to strong scattering including the peak of the intensity variance. Experimental values of the scintillation index are compared with classical theoretical predictions and also with the results of recent numerical simulations. The classical probability density functions (log-normal, exponential, I-K) are tested against the measured probability distributions. The generalized gamma distribution, which varies smoothly from log-normal to exponential as a function of two parameters, appears m represent the experimental data for a very large range of scattering conditions.     

Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence

By using the extended Huygens–Fresnel principle, the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived, and used to study the changes in spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and to compare the results of random electromagnetic GSM vortex-free beams. The influence of atmospheric turbulence on the spectral Stokes parameters is analyzed. The validity of our results is interpreted physically.